Drag reduction due to nonionic-type surfactants in turbulent pipe flow of ethylene glycol aqueous solution

In recent decades, the effect of surfactant additives on the rheological drag reduction has attracted considerable research interest. In particular, surfactants exhibit notable abilities, such as turbulent drag reduction and repairable self-assembly characteristics.^1–4 Typical drag-reducing cationic surfactants, such as cetyltrimethylammonium bromide (CTAB) and chloride (CTAC) in water, usually form network structures of micelles if an additive, e.g., sodium salicylate (NaSal), is mixed in the solution.^5,6 Chou et al.⁷ noted that different types of cationic surfactants, such as Ethoquad O/12 (Akzo Chemical), which mainly consists of oleyl-N, N-bis(2-hydroxyethyl)-N-methylammonium chloride, could reduce the friction drag of pipe flows in a recirculation pumping system at both high and low solution temperatures. Such cationic surfactants have been successfully implemented in district heating and cooling systems.^4,8

Compared to the cationic surfactants, drag-reducing nonionic-type surfactants of alkylamine N-oxide are more environmentally friendly owing to their nontoxic and biodegradable properties. In addition, these compounds can form network structures of threadlike micelles without any additive⁹ to reduce the friction drag in turbulent flows. Therefore, the drag reduction effect of nonionic-type surfactants (e.g., SPE95285, AKZO-Nobel Chemicals) has been a popular research subject (e.g., Refs. 10–13), following the pioneering study of Zakin et al.^14,15 Usui et al.¹⁶ and Tamano et al.^17,18 reported the drag-reducing ability of other kinds of nonionic-type surfactants (Aromox, LION AKZO Co., Ltd.) that mainly consisted of oleyl-N, N-dimethylamine N-oxide (ODMAO). A barrier to the application of drag-reducing additives for closed pipe flow systems is irreversible degradation.^13,19 Tamano et al.²⁰ highlighted that the addition of small amount of organic acids, such as salicylic and cuminic acids, to ODMAO solutions could significantly enhance the drag-reducing ability in the circuit pipe flow system involving a centrifugal pump, and the drag reduction could be maintained over a long period. Moreover, the authors indicated that the drag-reducing ability of ODMAO was comparable to or better than that of the typical cationic surfactant (Ethoquad O/12).

To facilitate the industrial application of surfactants as drag-reducing additives, it is necessary to examine their effectiveness in different types of solvents. Notably, the drag reduction performance of such surfactants in antifreeze solutions, such as ethylene glycol (EG) and propylene glycol (PG), is of significance to enable their use in cold weather regions. Zhang et al.²¹ reported that a high drag reduction ratio of up to ∼70% could be obtained in EG aqueous solutions (up to 28 wt. %) at a solution temperature of T = 20 °C if a cationic surfactant (Ethoquad O/12) with NaSal was introduced; moreover, the presence of EG enhanced the drag reduction ability. Nakamura et al.²² showed that the addition of PG of 10 wt. % deteriorated the drag reduction performance of Ethoquad O/12 at ∼T = 25 °C, compared to that in the case of water solvent. Wei et al.²³ showed that the newly synthesized zwitterionic surfactant (oleyl trimethylaminimide) provided the maximum drag reduction of more than 80% in a 20 wt. % EG aqueous solution at T = 25 °C, compared to that in the case of water flow. Haruki et al.^24,25 investigated the drag-reducing effect of the nonionic-type surfactant, oleyl-N, N-bis(2-hydroxyetyl)amine N-oxide (ODEAO), at low temperatures ranging between T = −20 and 5 °C in EG and PG aqueous solutions of up to 30 wt. % and clarified the difference in the effects of the solution temperature on the drag reduction in EG and PG aqueous solutions. In addition, Haruki and Horibe²⁶ investigated the effects of the flow drag and heat transfer of ODEAO in organic brine (potassium acetate) and inorganic brine (calcium chloride) solutions of up to 30 wt. % and highlighted the difficulty in practical use of ODEAO as heat transfer media in such organic and inorganic solutions; in particular, the flow drag and heat transfer reduction were observed only under certain conditions. Furthermore, Tamano et al.²⁷ indicated that the addition of a small amount of salicylic acid to ODMAO solutions significantly increased the drag-reducing ability for the ODMAO concentration of up to 3000 ppm by weight in even the 30 wt. % EG aqueous solution at T = 20 °C in pipe flow systems.

The previous studies on the drag reduction of different surfactants in different co-solvent solutions demonstrated their potential in industrial applications, such as direct cooling and heating systems; however, in most cases, the solution temperature was limited to approximately the room temperature or a relatively narrow range. In this context, the systematic accumulation of experimental data at various solution temperatures is of significance for further application of drag-reducing surfactants. Notably, in the experimental measurements of the flow rate and pressure drop, it is often challenging to accurately maintain the solution temperature in a wide range of less than 0 °C to near boiling temperature. Although we adopted heating and cooling systems in our previous experimental setups,^19,20,27 it was nearly impossible to uniformly maintain the temperature of the working fluids in all the parts—such as the pipe arrangement and upstream and downstream tanks—to be higher or lower than the room temperature.

Considering this aspect, in this study, we constructed a novel experimental apparatus to obtain measurements in a wide range of solution temperatures between T = −5 and 80 °C. Subsequently, the drag-reducing effects of two nonionic-type surfactants, specifically, ODMAO (which was adopted in the previous studies^20,27) and newly synthesized octadecyl-N, N-bis(2-hydroxyethyl)amine N-oxide (C18BAO), were systematically investigated in EG aqueous solutions at various surfactant concentrations and temperatures.

The remaining paper is organized as follows: Sec. II describes the drag-reducing agents and the novel experimental setup in which the temperature of the working fluids in pipe flows from laminar to turbulent regimes can be maintained at a constant and stable level, as well as the adopted methodologies and working fluids are described in. Section III presents the experimental results: The drag-reducing effect of ODMAO is first discussed, followed by the comparison of the effects of C18BAO and mixed surfactants. Section IV summarizes the key results and presents the concluding remarks.

Two kinds of nonionic-type surfactants of alkylamine N-oxide were used as drag-reducing agents. One surfactant was a generous gift as CADENAX DM10D-W (formerly known as AROMOX) from LION AKZO Co., Ltd., which mainly consisted of oleyl-N, N-dimethylamine N-oxide (ODMAO) [C₁₈H₃₅(CH₃)₂N → O] in isopropanol. The other surfactant was octadecyl-N, N-bis(2-hydroxyethyl)amine N-oxide (C18BAO) [C₁₈H₃₇(CH₂CH₂OH)₂N → O], which was prepared as follows: First, octadecyl-N, N-bis(2-hydroxyethyl)amine (C18BA) was prepared with 1-bromooctadecane and diethanolamine by the method of Kanetani et al.²⁸ The obtained compound of C18BA was treated with hydrogen peroxide, yielding C18BAO, by the method similar to that described by Cope and Ciganek.²⁹ 

1-Bromooctadecane (C₁₈H₃₇Br), diethanolamine [HN(CH₂CH₂OH)₂], and salicylic acid were obtained from Tokyo Chemical Industry Co. Ltd., Tokyo, Japan. Hydrogen peroxide was obtained from Wako Pure Chemical Industries Ltd., Osaka, Japan. As for the EG aqueous solution, ethylene glycol (HOCH₂CH₂OH, NACALAI TESQUE, INC) was adopted for the co-solvent.

We constructed a novel experimental apparatus for pipe flows involving a high-pressure syringe system, in which the pressure loss could be easily measured by maintaining the solution temperature constant in a wide range of temperatures at various flow rates. Such setups are helpful to assess the drag-reducing ability of surfactants, which is sensitive to the variation in the solution temperature.

Figure 1 shows the experimental setup, which consists of a test section pipe, thermostatic tank, and high-pressure micro feeder. Unlike the high-pressure tank used in our previous study,²⁷ in which the flow rate was required to be measured, the micro-feeder (Sanyo Technos Co., Ltd., JP-HR), which involves a stainless cylinder of 400 ml, controlled the extrusion rates between 0.01 and 1000 mm/min, corresponding to shear rates between 254 and 42 300 s⁻¹. The reliability of the flow rate was confirmed using the weighting method. As the operating principle, the working fluid was automatically sucked into the cylinder in the micro-feeder and later ejected into the stainless pipe at the set flow rate (extrusion rate) after switching over a three-way cock. The pressure drop was measured using a pressure transducer (Validyne Engineering Co., Ltd., DP15-40-N3S4A, full-scale 85 kPa) with an amplifier (Validyne Engineering Co., Ltd., PA501), and the output voltage was recorded using a multimeter with the auto-range functionality (Good Will Instrument Co., Ltd., GDM-8246). All the parts in contact with the working fluids involved stainless pipes that were connected with pressure-resisting ferrule structures. The internal diameter of the stainless pipe was d = 1.97 mm (nominal diameter was 2 mm). The developing region was 800 mm long (≃400 d), longer than that for a typical drag-reducing flow (≃100 d), as indicated by Gasljevic et al.;¹³ moreover, the measurement region was L = 100 mm long (≃50 d). The temperature of the working fluids T was controlled in the thermostatic tank (AS ONE Co., Ltd., LBX-350); in particular, in this setup, the working fluids could be cooled or heated in the range between T = −5 and 80 °C. To ensure that the solution temperature was within ±0.3 °C during measurements conducted in a wide range of temperature, most sections of the stainless pipes were covered with homemade water jacket structures pertaining to an additional thermostatic tank (TOKYO RIKAKIKAI Co., Ltd., NTT-20G or AS ONE Co., Ltd., ED-1), and the remaining parts of the plumbing system were covered with an adiabatic material (AS ONE Co., Ltd., Aeroflex Tube and Sheet).

The EG concentration was fixed at C_e = 30% by weight, which corresponded to the maximum concentration considered in previous studies.^21,26 The dependence of the drag-reducing effect of ODMAO on EG concentration C_e at the room temperature has been clarified in our previous work.²⁷ The ODMAO solution concentrations were set as 100, 500, 1000, 1500, and 2000 ppm by weight. In the case of ODMAO aqueous solution, the addition of a small amount of salicylic acid with a molar ratio of ξ = 0.2 enhances the drag-reducing effect;^20,27 this aspect has also been highlighted by Usui et al.,¹⁶ who used NaSal as an additive to the ODMAO solution. Furthermore, salicylic acid was added to EG aqueous solution because no drag reduction was observed in its absence (see also Ref. 27). The C18BAO solution concentrations were set as 10, 50, 100, 500, 1000, 1500, and 2000 ppm by weight. Unlike ODMAO, C18BAO did not require the addition of the organic acid, and any such addition deteriorated the drag reduction performance. The surfactants, ODMAO (with or without salicylic acid) or C18BAO, were poured into 13.5 l water or EG aqueous solution in the thermostatic tank. Next, while maintaining the solution temperature at ∼80 °C, the fluids were sufficiently mixed until the white turbidity completely disappeared for approximately one hour. Thereafter, the solution temperature was set to the target value.

In this setup, because a thermostatic tank was utilized as both the upstream and downstream tank, the working fluid was likely influenced by the high shear stress in the pipe during measurements. Nevertheless, the considered nonionic-type surfactants were not likely to be as degraded as a typical drag-reducing polymer, and their robustness was superior to that of a typical drag-reducing cationic surfactant.²⁰ We confirmed that there was no discernible difference in the drag-reducing ability of the adopted ODMAO and C18BAO even after more than 100 trials (not shown herein). In other words, the degradability tendency of present nonionic-type surfactant solutions did not invalidate the experimental results.

The shear viscosity η and shear rate $γ̇$ were investigated for the individual and mixed surfactants by using both a cone-and-plate type viscometer (TOKI SANGYO Co., Ltd., TPE-100) and capillary viscometer in order to obtain the data over four orders of magnitude of shear rate. The cone diameter was 24 mm, and the cone angle was 1°34′. The current setup for the pipe flow system with a small diameter (d = 1.97 mm) was utilized as the capillary viscometer, and thus, the resultant shear viscosity was evaluated as the apparent value.

The Reynolds numbers, which are based on the fluid properties of solvents, were denoted by Re_w and Re_e for water and EG aqueous solution, respectively, and defined as follows:

where U_m is the bulk velocity of the pipe flow and fixed at the corresponding Reynolds number. ρ and η denote the density and shear viscosity of the solvent, respectively. The subscripts “w” and “e” denote fluid properties of water and EG aqueous solution, respectively. Re_w and Re_e can help evaluate the drag-reducing ability of surfactant solutions with the variations in the shear viscosity, as reported in a previous study.² To evaluate the drag-reducing ability under variations in the shear viscosity with the shear rate, the values of ρ and η of water or EG aqueous solution were considered for the surfactant solutions at the same temperature, as reported in a previous study.² The values of ρ and η for water or EG aqueous solution at different temperatures were obtained through the polynomial approximation derived using the available data pertaining to the physical properties.

The friction factor λ is defined as follows:

where ΔP is the pressure difference between L = 100 mm (≃50 d), as shown in Fig. 1.

The drag reduction ratio DR for the pipe flow is defined as follows:

where λ and λ_s are the friction factors of the surfactant solutions and solvent (Newtonian fluid), respectively, estimated using the Blasius relation at the corresponding Reynolds number Re_w or Re_e.

First, the effect of the concentration of ODMAO on the drag reduction in water as a solvent at T ≃ 20 °C is discussed about the relation between λ and Re_w [Fig. 2(a)]. The ODMAO concentrations, C_s, were 100, 500, 1000, 1500, and 2000 ppm by weight, corresponding to 4, 22, 43, 65, and 87 mM, respectively. In Fig. 2(a), the dotted, dashed, and solid lines represent the Hagen–Poiseuille laminar theoretical relation (λ = 64/Re_w), the Blasius experimental relation $(λ=0.3164Rew−0.25)$ for Newtonian fluids, and Zakin’s maximum drag reduction asymptote (MDRA) for the surfactant solutions $(λ=1.28Rew−0.55)$⁠,² respectively. The preset data for water (C_s = 0 ppm) agree with both the laminar theoretical and turbulent empirical relations, thereby demonstrating the reliability and accuracy of the obtained measurements. We also confirmed the high level of reproducibility through the several time measurements. The data at C_s = 100 ppm agree with those of water in both laminar and turbulent regions, indicating that no drag reduction occurred. For ODMAO solutions with C_s ranging from 500 to 2000 ppm, the relation between λ and Re_w exhibits a smooth transition from laminar to drag-reducing turbulent flows, indicating that the transition is delayed to higher Reynolds numbers. Such behavior is characteristic of Virk’s type B drag reduction^12,30 in which asymptotic drag reduction occurs immediately after transition from laminar to turbulent flows. As the ODMAO concentration increases, the relation between λ and Re_w shifts upward with respect to the Hagen–Poiseuille laminar theoretical relation in the low-Reynolds number region. This phenomenon occurs at higher ODMAO concentrations because of the larger increase in the shear viscosity compared to that of water.

Furthermore, as shown in Fig. 2(a), the friction factor monotonically decreases as the Reynolds number increases to a critical value of Re_c, at which the friction factor is minimized and then suddenly increases, leading to the maximum drag reduction ratio. In the case of Newtonian fluids, the critical Reynolds number is that at which the flow changes from laminar to turbulent. In the considered experimental setup, Re_c is ∼2000 for water. As the ODMAO concentration increases, Re_c increases, corresponding to the transition delay from laminar to turbulent flows [the details are shown in Fig. 4(a)]. Notably, this case corresponds to Virk’s type B drag reduction. In the case of Virk’s type A drag reduction,^12,30 in which the friction coefficient approaches the Newtonian (Blasius) line beyond a certain Reynolds number and subsequently decreases as the Reynolds number increases, the Reynolds number at the maximum drag reduction ratio is not necessarily the critical Reynolds number. Beyond Re_c, the friction factor suddenly increases and approaches the Blasius experimental relation. This disappearance of the drag reduction is attributable to the breakdown of the network structures of surfactant micelles and not the destruction of micelles, according to the repairable drag-reducing ability.²⁰ 

Figure 2(b) shows that the drag reduction ratio DR increases with the increase in Re_w and reaches the maximum value DR_max at Re_c. Subsequently, the drag reduction ratio decreases sharply as the Reynolds number increases and later stabilizes to zero, corresponding to the asymptotic behavior of the friction factor λ to the Blasius equation [cf. Fig. 2(a)]. With the increase in the ODMAO concentration, DR_max approaches the Zakin’s MDRA relation [Fig. 2(b)]. For the present water solvent, the highest drag reduction ratio occurs at C_s = 2000 ppm, at which DR_max is 64% at Re_w ≃ 9100.

Next, the drag-reducing effect of ODMAO in EG aqueous solution is considered. Figures 3(a) and 3(b) show the relation of λ and DR against Re_e, respectively, at T ≃ 20 °C in EG (C_e = 30%) aqueous solution. The ODMAO concentrations are C_s = 500, 1000, 1500, and 2000 ppm by weight. In the case of EG aqueous solution, a small amount of salicylic acid is introduced, with the optimal molar ratio to ODMAO being approximately ξ = 0.2^20,27 to realize drag reduction. For EG aqueous solution without ODMAO (C_s = 0 ppm), the data agree with the Hagen–Poiseuille and Blasius relations in both the laminar and turbulent regions, respectively, demonstrating the accuracy of the obtained measurements. At C_s = 500 ppm, the relation between λ and Re_e is in agreement with the Hagen–Poiseuille relation in the laminar region, and λ is slightly larger than that of the Blasius relation in the turbulent region, corresponding to the slight increase in the friction drag. This is due to the slight increase in shear viscosity. At C_s = 1000 ppm, the small drag reduction ratio of less than 10% is obtained. At C_s = 1500 ppm, the drag reduction ratio exceeds 40%, which is still considerably smaller than that in the case of water solvent, and the range of the Reynolds number for the drag reduction is narrower [cf. Fig. 2(b)]. At C_s = 2000 ppm, DR_max = 59% is observed at Re_e ≃ 6100. The drag-reducing performance at C_s = 2000 ppm is comparable with that of the corresponding water solvent [cf. Fig. 2(b)].

To compare the dependence of the drag-reducing ability on the ODMAO concentration C_s in water and EG (C_e = 30%) aqueous solution, the effects of C_s on Re_c and DR_max at T ≃ 20 °C were considered, as illustrated in Figs. 4(a) and 4(b), respectively. In the case of water solvent, Re_c increases monotonically with the increase in the ODMAO concentration [Fig. 4(a)]. In the case of EG aqueous solution, Re_c increases gradually with the ODMAO concentration from C_s = 500 to 1500 ppm and sharply from C_s = 1500 to 2000 ppm. The value of Re_c in EG aqueous solution is considerably smaller than that in water at the corresponding ODMAO concentration. For example, the Re_c value of water at C_s = 1000 ppm is almost the same as that of EG aqueous solution at C_s = 2000 ppm. In other words, in the case of EG (C_e = 30%) aqueous solution, the amount of ODMAO required is two times that required for water at the same Re_c. Furthermore, because a higher critical Reynolds number implies that the connections of the surfactant micelles are stronger, the network structures of micelles are likely weaker in EG aqueous solution than those in pure water solvent solution.

Figure 4(b) shows that DR_max for water is considerably larger than that for EG aqueous solution. In the case of water solvent, at C_s = 100 ppm, no drag reduction occurs, i.e., DR_max is zero. Notably, DR_max gradually increases as the ODMAO concentration increases to C_s = 1000 ppm and only slightly increases as the concentration increases to 2000 ppm. In contrast, in the case of EG aqueous solution, DR_max is zero below C_s = 500 ppm, and its value gradually increases as the ODMAO concentration increases to C_s = 2000 ppm. Moreover, Fig. 4 shows that the addition of EG to water decreases the effect of ODMAO as a drag-reducing additive. This phenomenon is in contrast to the findings of Haruki et al.,²⁴ who reported that the addition of EG enhances the drag-reducing ability of ODEAO. The ODMAO is very weakly positively charged in water so that the negatively charged counterion, i.e., salicylic acid, encourages the formation of micelles.^16,20 On the other hand, EG has the hydrophobic property that leads to inhibition of the formation of micelles. In EG aqueous solution, therefore, the drag-reducing effect of ODMAO could become weaker if the effect of hydrophobic property due to EG is larger than that of neutralization due to salicylic acid.²⁷ The effect of the addition of EG on the drag reduction of ODEAO is discussed later.

Next, the effect of T on the drag-reducing ability of ODMAO is examined. Figures 5(a) and 5(b) show the relationship of λ and DR against Re_w, respectively, for the range T ≃ 2–70 °C at the ODMAO concentration of C_s = 2000 ppm in water. It can be noted that drag reduction occurs for all the considered solution temperatures. In particular, for the range of T ≃ 20–60 °C, an extremely high drag reduction ratio exceeding 60% is achieved. At T ≲ 50 °C, Virk’s type A drag reduction is observed, whereas Virk’s type B drag reduction is observed at T ≃ 70 °C. At T ≃ 60 °C, two minima of the friction factor, i.e., two maximum drag reduction ratios, are observed, and the corresponding behavior is intermediate to Virk’s type A and B effects. This phenomenon indicates that the drag reduction type can be altered according to the solution temperature, even if the same surfactant is used under the same concentration in the same experimental setup (see also Ref. 19). Even at the lowest and highest solution temperatures of T ≃ 2 and 70 °C, respectively, the maximum drag reduction exceeds 50%, which verifies that the nonionic-type surfactant ODMAO can considerably reduce the drag in pure water solvent (see also Ref. 20).

To clarify the drag-reducing performance in EG aqueous solution, the effect of the solution temperature on the drag reduction in EG (C_e = 30%) aqueous solution is investigated. Figures 6(a) and 6(b) show the relationship of λ and DR against Re_e, respectively, for the range T ≃ −5–50 °C at C_s = 2000 ppm with salicylic acid (ξ = 0.2). Except at T ≃ 50 °C, the drag reduction occurs. At T ≤ 30 °C, the relation between λ and Re_e corresponds to Virk’s type B drag reduction behavior. At T ≃ 40 °C, the drag reduction exhibits Virk’s type A behavior. Notably, even at T ≃ −5 °C, the drag reduction ratio exceeds 40%, although the range of Re_e for the drag reduction is narrow. This finding suggests that ODMAO is an effective drag reduction agent in the low temperature range under 40 °C in both EG aqueous solution and water solvent.

For the case of ODMAO (C_s = 2000 ppm) in EG (C_e = 30%) aqueous solution with salicylic acid (ξ = 0.2), the relations of Re_c and DR_max against T are shown in Figs. 7(a) and 7(b), respectively. At T ≃ 60 °C, at which the transition from Virk’s type B to A may occur, two values of Re_c (≃5300 and 35 000) and corresponding DR_max (=27% and 69%) are observed [see also Figs. 5(a) and 5(b)]. Only the second Re_c and DR_max are plotted in Figs. 7(a) and 7(b), respectively, as this discussion is performed focusing on Virk’s type A drag reduction behavior.

Figure 7(a) shows that Re_c for water and EG aqueous solution are comparable in the low temperature region, below T ≃ 10 °C. In the case of EG aqueous solution, Re_c increases with the increase in T; in particular, the value sharply increases from T ≃ 30 to 50 °C. At T ≃ 70 °C, the drag reduction behavior corresponds to Virk’s type B, and Re_c is ∼2000. Overall, the Re_c value of water solvent is considerably larger than that of EG aqueous solution. Furthermore, Fig. 7(b) shows that a sufficiently high value of DR_max can be obtained in a wide range of the solution temperature for water solvent. In contrast, for EG aqueous solution, DR_max up to T ≃ 20 °C is comparable to that of water solvent, and beyond T ≃ 30 °C, the value drastically decreases with increasing T, and the drag-reducing ability disappears at T ≃ 50 °C. Without the salicylic acid (ξ = 0.2), drag reduction cannot be realized in EG aqueous solution, unlike in water solvent.

The findings presented in Fig. 7 demonstrate that the performance of ODMAO in EG aqueous solution is inferior to that in water solvent, even if salicylic acid is used. Considering the inferior drag-reducing performance of ODMAO in EG aqueous solution in the high temperature region, the drag-reducing effect of the other nonionic-type surfactant, C18BAO, is examined at various surfactant concentrations and solution temperatures.

Figure 8 shows the effects of C18BAO concentration up to C_s = 1000 ppm on λ vs Re_w in aqueous solutions at a relatively high T ≃ 60 °C. The concentrations of C18BAO are 10, 50, 100, 500, and 1000 ppm by weight, corresponding to 0.4, 1.8, 3.6, 18, and 36 mM, respectively. As shown in Fig. 8, the data regarding C18BAO agree with the Hagen–Poiseuille and Blasius equations in both laminar and turbulent regions, respectively; thus, C18BAO does not lead to any drag reduction in water at T ≃ 60 °C. In contrast, the drag-reducing effect in EG aqueous solution at the same temperature is significant, as discussed below.

Figure 9 shows the drag-reducing effect of C18BAO with a concentration of up to C_s = 2000 ppm in EG (C_e = 30%) aqueous solution at T ≃ 60 °C. The concentrations of C18BAO are 500, 1000, 1500, and 2000 ppm by weight. Figures 9(a) and 9(b) illustrate the effects on the relations between λ and Re_e and between DR and Re_e, respectively. The drag-reducing effect is observed in the complete range of C_s = 500–2000 ppm. To quantitatively evaluate this effect, the influence of C18BAO concentration C_s on Re_c and DR_max is visualized, as shown in Fig. 10. Re_c gradually increases with the increase in C_s. In contrast, DR_max sharply increases up to C_s = 500 ppm and then gradually increases with increasing C_s, with saturation observed at C_s = 2000 ppm. This finding is the first evidence that the nonionic-type surfactant C18BAO exhibits a prominent drag-reducing ability in EG aqueous solution. Notably, the superior drag-reducing performance of C18BAO in EG aqueous solution compared to that in water solvent is consistent with the finding of Haruki et al.²⁴ for a different type of nonionic-type surfactant, ODEAO. Haruki et al.²⁴ claimed that the hydrogen bonding between the two hydroxy groups of EG and hydrophilic groups of ODEAO contributes to the formation of large network structures of micelles, leading to the strengthening of the shear induced structures. The chemical structure of C18BAO is similar to that of ODEAO so that the drag-reducing mechanism of C18BAO in EG aqueous solution is almost the same as that of ODEAO, i.e., the hydrogen bonding between two hydroxy groups of EG and hydrophilic groups of C18BAO facilitates the formation of network structures of micelles. Moreover, it can be deduced that the difference in the effect of EG on the drag reduction between ODMAO and C18BAO (or ODEAO) is attributable to the difference in chemical structures in which ODMAO does not involve hydroxyethyl groups but C18BAO (or ODEAO) does.

Figure 11 shows the relation between λ and Re_w for the C18BAO aqueous solution at C_s = 1000 ppm at a high temperature range from T ≃ 40 to 80 °C. All the data collapse on the Hagen–Poiseuille and Blasius equations in the wide range of Reynolds number from laminar to turbulent regions, and thus, no drag reduction is observed at the considered solution temperatures. The findings shown in Figs. 8 and 11 demonstrate that C18BAO does not exhibit any drag-reducing ability in water solvents, regardless of the solution concentration and temperature.

Figures 12(a) and 12(b) show the relations between λ and Re_e and between DR and Re_e, respectively, for the case of C18BAO (C_s = 2000 ppm) in EG (C_e = 30%) aqueous solution in the range from T = 40 to 80 °C. At T = 40 °C, the friction factor is larger than the Blasius equation at the corresponding Reynolds number, i.e., the friction drag increases, and the drag reduction ratio is negative. Moreover, white turbidity of the solution is observed in the quartz beaker as the temperature is decreased using a hot stirrer and temperature-controlled water tank; it is noted that the Krafft point of C18BAO is ∼49 °C at C_s = 2000 ppm in the case of EG 30% aqueous solution. Therefore, at T = 40 °C, the drag-reducing ability is likely to disappear owing to the precipitation of C18BAO. However, from T = 50 to 80 °C, Virk’s type B behavior is observed, and the drag reduction ratio exceeds 60%. This finding verifies that C18BAO is a promising drag-reducing additive for EG aqueous solution in the high temperature range exceeding T = 50 °C, although it does not lead to any drag reduction for water at the same temperature (see also Fig. 11).

Figure 13 shows the effect of the solution temperature range between T = 40 and 80 °C on Re_c and DR_max in the case of C18BAO (C_s = 2000 ppm) in EG (C_e = 30%) aqueous solution. There, Re_c monotonically increases as T increases. This implies that the effective Reynolds number range for drag reduction becomes wider at the higher solution temperature. DR_max is ∼70% at T greater than 50 °C. This finding pertains to the first evidence of C18BAO demonstrating excellent drag reduction at high temperatures in EG aqueous solution, as mentioned previously.

According to the experimental data, in the case of EG 30% aqueous solution, the mixture of ODMAO with salicylic acid with a molar ratio of ξ = 0.2 is effective in the low temperature range of up to T ≃ 40 °C, whereas C18BAO is effective at high temperatures exceeding T ≃ 50 °C. Next, the synergetic effect of ODMAO and C18BAO in EG aqueous solution is considered. In the wide range of solution temperatures from T ≃ −5 to 80 °C, the relations between λ and Re_e and between DR and Re_e are shown in Figs. 14(a) and 14(b), respectively, in the mixture of ODMAO (C_s = 2000 ppm) with salicylic acid (ξ = 0.2) and C18BAO (C_s = 2000 ppm) in EG (C_e = 30%) aqueous solution. Figure 14(a) shows that the relation between λ and Re_e corresponds to Virk’s type B and A behavior at the solution temperature ranging between T ≃ −5 and 60 °C and at T ≃ 70 and 80 °C, respectively. As the solution temperature is increased from T ≃ −5–60 °C, the range of Re_e for the distinct drag reduction increases. At T ≃ 30–50 °C, the drag reduction ratio approaches Zakin’ MDRA. At T ≃ 70 and 80 °C, two minima of λ, i.e., two maxima of DR, appear owing to Virk’s type A drag-reducing behavior. The drag-reducing ability drastically decreases at T ≃ 70 °C and almost disappears at T ≃ 80 °C.

Figure 15 shows the effect of T on Re_c and DR_max in the mixture of ODMAO (C_s = 2000 ppm) with salicylic acid (ξ = 0.2) and C18BAO (C_s = 2000 ppm) in EG (C_e = 30%) aqueous solution. In the case of Virk’s type A behavior at T ≃ 70 and 80 °C, in which two Re_c and DR_max are observed, only the larger Re_c and corresponding DR_max are plotted in Fig. 15, as in the case of ODMAO aqueous solution (see Fig. 7). DR_max is maximized at ∼T ≃ 40 °C and reduces beyond T ≃ 60 °C. Re_c monotonically increases with the increase in T. Notably, at T ≃ 40 °C, the maximum drag reduction ratio of a single surfactant is considerably smaller for individual case of ODMAO and C18BAO [see also Figs. 7(b) and 13]. This finding implies that the drag-reducing performance is enhanced by certain synergetic effects of the mixed surfactants. Broniarz-Press et al.³¹ reported that a mixed drag reducer system (polymer/surfactant or surfactant/surfactant) can help increase the system stability and temperature range in which the additives are most effective. This phenomenon likely occurs in the case of present nonionic-type surfactants of ODMAO and C18BAO. In this study, combining ODMAO and C18BAO results in the decrease in the Krafft point compared to that of C18BAO, and then the preferable effect due to the hydrogen bonding between hydroxyethyl groups of C18BAO and hydroxy groups of EG is likely to emerge for the mixture of ODMAO and C18BAO. However, DR_max for the mixture of ODMAO and C18BAO is smaller than that of ODMAO below T ≃ 0 °C [cf. Fig. 7(b)] and that of C18BAO beyond T ≃ 60 °C (cf. Fig. 13).

To further examine the synergetic drag-reducing effects of ODMAO and C18BAO in EG aqueous solution, Figs. 16 and 17 show the relation between the shear viscosity η and shear rate $γ̇$ for the case of ODMAO (C_s = 2000 ppm) with salicylic acid (ξ = 0.2) and the case of C18BAO (C_s = 2000 ppm), respectively, in EG (C_e = 30%) aqueous solution. Figure 18 shows the effect of the solution temperature ranging from T ≃ −5 to 80 °C on the relation between η and $γ̇$ in the mixture of ODMAO (C_s = 2000 ppm) with salicylic acid (ξ = 0.2) and C18BAO (C_s = 2000 ppm) in EG (C_e = 30%) aqueous solution. The data pertaining to the cone-and-plate type viscometer are smoothly connected to those pertaining to the capillary viscometer for ODMAO (see Fig. 16), indicating the absence of any size effect. In contrast, distinct gaps can be observed for C18BAO (see Fig. 17). The largest gap, which occurs at T ≃ 40 °C, can likely be attributed to the effect of precipitation due to the Krafft point of C18BAO, as illustrated in Fig. 12. In the case of ODMAO in EG aqueous solution (Fig. 16), the shear viscosity is Newtonian-like, i.e., independent of the shear rate at T ≃ 40 and 50 °C, although shear-thinning behavior is observed at low temperatures from T ≃ 30 to −5 °C; at the low temperatures, the degree of shear-thinning increases as the solution temperature decreases. In contrast, in the case of C18BAO in EG aqueous solution (Fig. 17), primarily shear-thinning is observed, regardless of the solution temperature between T ≃ 40 and 80 °C. In the case of the mixture of ODMAO and C18BAO in EG aqueous solution (Fig. 18), both shear-thinning and shear-thickening are observed at T ≃ 10, 20, and 30 °C; in particular, the shear viscosity gradually decreases with increasing T, although several gaps can be observed between the data of the cone-and-plate and capillary viscometers. At T ≃ 40 °C, only shear-thinning is observed in the higher shear rate region, and the shear viscosity is larger than that at T ≃ 30 °C in the small shear rate region. In the higher temperature range from T ≃ 50 to 80 °C, slight shear-thickening behavior re-emerges, with the shear viscosity gradually decreasing with increasing T. The shear viscosity measurements show that the micellar solution exhibits the high sensitivity to solution temperature at T ≃ 40 °C. However, the drag-reducing behavior remains unchanged at T ≃ 40 °C, i.e., the drag-reducing type is the same, as well as the maximum drag reduction ratio, as shown in Figs. 14 and 15. This finding suggests that the drag reduction effects of nonionic-type surfactant solutions cannot be comprehensively assessed considering only the rheological properties based on the shear viscosity measurements, as also highlighted by Tamano et al.^19,20

The drag-reducing performance of two types of nonionic-type surfactants of alkylamine N-oxide, i.e., ODMAO and newly synthesized C18BAO was comprehensively investigated in EG aqueous solution (30% by weight) for turbulent pipe flow. In particular, the inner diameter of the pipe was 2 mm, and a novel experimental setup was established, involving a high-pressure micro-feeder and wide-range temperature control system. The surfactant concentrations were varied up to 2000 ppm by weight, and the solution temperatures were varied from −5 to 80 °C. As the drag-reducing additive in EG 30% aqueous solution, the mixture of ODMAO with salicylic acid with a molar ratio of 0.2 was effective in the lower temperature range up to 40 °C, whereas C18BAO was effective at higher temperatures exceeding 50 °C. Compared to the effect of the individual surfactant, the mixture of ODMAO and C18BAO in EG aqueous solution exhibited excellent drag reduction exceeding 60% in a wide range of solution temperature ranging between 20 and 60 °C, likely owing to a synergetic effect, although the drag reduction performance deteriorated below 0 °C and beyond 60 °C. The presented findings can facilitate the optimization of the drag reduction effect for a certain range of solution temperatures in EG aqueous solution.

We believe that the considered environmentally friendly nonionic-type surfactants are promising candidates as drag-reducing additives in EG aqueous solution in addition to cationic and zwitterionic surfactants.^21,23 Furthermore, this research can provide guidance for the development of mixed drag-reducing surfactants, as highlighted by Broniarz-Press et al.³¹ Nevertheless, further investigation must be performed at various ratios of concentrations of ODMAO and C18BAO to clarify the mechanism of the synergetic effects and enable their application in practical energy-saving systems^8,32 in co-solvent solutions, such as EG and PG aqueous solutions.

This work was partially supported by a Grant-in-Aid for Scientific Research (Grant No. JP15H03918) from the Japan Society for the Promotion of Science. Furthermore, we thank Lion Specialty Chemicals Co., Ltd. for providing the surfactants.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.